Tagged: conditional probability

Problem 737

Two fair coins are tossed. Given that at least one of them lands heads, what is the conditional probability that the first coin lands heads?

Problem 736

Let $C$ be the event that a randomly chosen person has lung cancer. Let $S$ be the event of a person being a smoker.
Suppose that 10% of the population has lung cancer and 20% of the population are smokers. Also, suppose that we know that 70% of all people who have lung cancer are smokers.

Then determine the probability of a person having lung cancer given that the person is a smoker.

Problem 732

A card is chosen randomly from a deck of the standard 52 playing cards.

Let $E$ be the event that the selected card is a king and let $F$ be the event that it is a heart.

Prove or disprove that the events $E$ and $F$ are independent.

Problem 731

A jewelry company requires for its products to pass three tests before they are sold at stores. For gold rings, 90 % passes the first test, 85 % passes the second test, and 80 % passes the third test. If a product fails any test, the product is thrown away and it will not take the subsequent tests. If a gold ring failed to pass one of the tests, what is the probability that it failed the second test?

Problem 730

Four fair coins are tossed.

(1) What is the probability that all coins land heads?

(2) What is the probability that all coins land heads if the first coin is heads?

(3) What is the probability that all coins land heads if at least one coin lands heads?

Problem 729

There are three blue balls and two red balls in a box.

When we randomly pick two balls out of the box without replacement, what is the probability that both of the balls are red?

Problem 728

A fair six-sided die is rolled.

(1) What is the conditional probability that the die lands on a prime number given the die lands on an odd number?

(2) What is the conditional probability that the die lands on 1 given the die lands on a prime number?